Question

Triangle ABC is shown below.

Triangle ABC; line passes through points D, B, and E
Given: ∆ABC

Prove: All three angles of ∆ABC add up to 180°.

The flow chart with missing reason proves the measures of the interior angles of ∆ABC total 180°.

Which reason can be used to fill in the numbered blank space?

Associative Property of Addition

Triangle Exterior Angle Theorem

Angle Addition Postulate

Commutative Property of Addition

Answer 1

To prove that all three angles of a triangle add up to 180°, the Triangle Exterior Angle Theorem is used, which supports the fact that the sum of the interior angles equals the straight angle on a line.

Step-by-step explanation:

The question you've asked is about proving that all three angles of a triangle add up to 180°. To do this, one can use the Triangle Exterior Angle Theorem. This theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. Because of this theorem, we know that the straight line formed by extending one side of the triangle must result in the exterior angle and the adjacent interior angle summing up to 180°. As the exterior angle is equal to the sum of the other two interior angles, it can be concluded that all three interior angles add up to 180°.